Question

\[ (1/x^{a-b})^{\frac{1}{a-c}} (1/x^{b-c})^{\frac{1}{b-a}} (1/x^{c-a})^{\frac{1}{c-b}} \]

Solution

\[ = x^{-\frac{a-b}{a-c}} \cdot x^{-\frac{b-c}{b-a}} \cdot x^{-\frac{c-a}{c-b}} \] \[ = x^{-\left[\frac{a-b}{a-c} + \frac{b-c}{b-a} + \frac{c-a}{c-b}\right]} \] \[ = x^{-(1+1+1-2)} = x^{0} \] \[ = 1 \]

Answer

\[ \boxed{1} \]

Next Question / Full Exercise